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            <h1>線形バイアスによる注意 (AliBi)</h1>
<p>これは、「<a href="https://papers.labml.ai/paper/2108.12409">トレインショート、テストロング」という論文の「線形バイアスによる注意（AliBi）」の実装です。線形バイアスによる注意により、入力の長さの推定が可能になります</a>。</p>
<p>これにより、位置エンコーディングがアテンションスコア（ソフトマックスの前のアテンションロジット）にバイアスが加わったものに置き換わります。これは自己回帰タスクでテストされた相対的なスキームで、近くにあるトークンの方がバイアスが大きく、遠いトークンの方がバイアスが低くなります。対数スケールでは（ソフトマックスの前なので）バイアスは直線的に減少し、各ヘッドの傾きは異なります</p>。
<p><span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em;"></span><span class="mord coloredeq equ" style=""><span class="mord mathnormal" style="">i</span></span></span></span></span></span>-th トークンのアテンションフォーミュラは次のとおりです。</p>
<span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:5.40006em;vertical-align:-2.45003em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.95003em;"><span style="top:-4.95003em;"><span class="pstrut" style="height:3.45em;"></span><span class="mord"><span class="mord"><span class="mord mathbf">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq equ" style=""><span class="mord mathnormal mtight" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-2.2500000000000004em;"><span class="pstrut" style="height:3.45em;"></span><span class="mord"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:2.45003em;"><span></span></span></span></span></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.95003em;"><span style="top:-4.95003em;"><span class="pstrut" style="height:3.45em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord coloredeq eqn" style=""><span class="mord text" style=""><span class="mord" style=""><span class="mord coloredeq eqp" style="">soft</span><span class="mord coloredeq eqp" style=""><span class="mord coloredeq eqv" style="">m</span></span><span class="mord coloredeq eqp" style="">ax</span></span></span></span><span class="mord"><span class="delimsizing size3">(</span></span><span class="mord"><span class="mord mathbf">q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq equ" style=""><span class="mord mathnormal mtight" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathbf">K</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8991079999999999em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">⊤</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord coloredeq eqv" style=""><span class="mord mathnormal" style="">m</span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord"><span class="delimsizing size1">[</span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mopen">(</span><span class="mord coloredeq equ" style=""><span class="mord mathnormal" style="">i</span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord">1</span><span class="mclose">)</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="minner">…</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord">0</span><span class="mord"><span class="delimsizing size1">]</span></span><span class="mord"><span class="delimsizing size3">)</span></span></span></span><span style="top:-2.2500000000000004em;"><span class="pstrut" style="height:3.45em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord coloredeq eqn" style=""><span class="mord text" style=""><span class="mord" style=""><span class="mord coloredeq eqp" style="">soft</span><span class="mord coloredeq eqp" style=""><span class="mord coloredeq eqv" style="">m</span></span><span class="mord coloredeq eqp" style="">ax</span></span></span></span><span class="mord"><span class="delimsizing size3">(</span></span><span class="mord"><span class="mord mathbf">q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq equ" style=""><span class="mord mathnormal mtight" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathbf">K</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8991079999999999em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">⊤</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord coloredeq eqv" style=""><span class="mord mathnormal" style="">m</span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord"><span class="delimsizing size1">[</span></span><span class="mord">0</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="minner">…</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mopen">(</span><span class="mord coloredeq equ" style=""><span class="mord mathnormal" style="">i</span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord">1</span><span class="mclose">)</span><span class="mord"><span class="delimsizing size1">]</span></span><span class="mord"><span class="delimsizing size3">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:2.45003em;"><span></span></span></span></span></span></span></span></span></span></span></span></span><p>ここで、<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.7335400000000001em;vertical-align:-0.19444em;"></span><span class="mord"><span class="mord mathbf">q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq equ" style=""><span class="mord mathnormal mtight" style="">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">∈</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.849108em;vertical-align:0em;"></span><span class="mord"><span class="mord mathbb">R</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.849108em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqt" style=""><span class="mord mathnormal mtight" style="">d</span></span></span></span></span></span></span></span></span></span></span></span></span>は <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em;"></span><span class="mord coloredeq equ" style=""><span class="mord mathnormal" style="">i</span></span></span></span></span></span>-th トークンのクエリ、<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.72243em;vertical-align:-0.0391em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">K</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">∈</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.8491079999999999em;vertical-align:0em;"></span><span class="mord"><span class="mord mathbb">R</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8491079999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight coloredeq equ" style=""><span class="mord mathnormal mtight" style="">i</span></span><span class="mbin mtight">×</span><span class="mord mtight coloredeq eqt" style=""><span class="mord mathnormal mtight" style="">d</span></span></span></span></span></span></span></span></span></span></span></span></span></span>までのキー<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em;"></span><span class="mord coloredeq equ" style=""><span class="mord mathnormal" style="">i</span></span></span></span></span></span>、<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord coloredeq eqt" style=""><span class="mord mathnormal" style="">d</span></span></span></span></span></span>およびヘッドあたりのフィーチャ数です。<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord coloredeq eqn" style=""><span class="mord text" style=""><span class="mord" style=""><span class="mord coloredeq eqp" style="">soft</span><span class="mord coloredeq eqp" style=""><span class="mord coloredeq eqv" style="">m</span></span><span class="mord coloredeq eqp" style="">ax</span></span></span></span></span></span></span></span>上記の等式は変換に不変であるため中止されることに注意してください (結果を変更せずにすべての要素に任意の定数を追加できます</p>)。
<p>AliBi <a href="experiment.html">モデルのトレーニングコードは次のとおりです</a>。</p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">33</span><span></span><span class="kn">import</span> <span class="nn">math</span>
<span class="lineno">34</span><span class="kn">from</span> <span class="nn">typing</span> <span class="kn">import</span> <span class="n">Optional</span>
<span class="lineno">35</span>
<span class="lineno">36</span><span class="kn">import</span> <span class="nn">torch</span>
<span class="lineno">37</span><span class="kn">from</span> <span class="nn">torch</span> <span class="kn">import</span> <span class="n">nn</span>
<span class="lineno">38</span>
<span class="lineno">39</span><span class="kn">from</span> <span class="nn">labml.logger</span> <span class="kn">import</span> <span class="n">inspect</span>
<span class="lineno">40</span><span class="kn">from</span> <span class="nn">labml_nn.transformers.mha</span> <span class="kn">import</span> <span class="n">MultiHeadAttention</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-1'>
        <div class='docs doc-strings'>
            <div class='section-link'>
                <a href='#section-1'>#</a>
            </div>
            <h2><span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord coloredeq eqv" style=""><span class="mord mathnormal" style="">m</span></span></span></span></span></span>各頭部の頭部固有の勾配を取得</h2>
<ul><li><code  class="highlight"><span></span><span class="n">n_heads</span></code>
アテンションレイヤーのヘッド数です <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord coloredeq eqw" style=""><span class="mord mathnormal" style="">n</span></span></span></span></span></span></li></ul>
<p>1 番目のヘッドの勾配は</p>
<p><span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:2.15101em;vertical-align:-0.82957em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.17043em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord coloredeq eqr" style=""><span class="mord" style="">2</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.93957em;"><span style="top:-3.3485500000000004em;margin-right:0.05em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mopen nulldelimiter sizing reset-size3 size6"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8443142857142858em;"><span style="top:-2.656em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqw" style=""><span class="mord mathnormal mtight" style="">n</span></span></span></span></span><span style="top:-3.2255000000000003em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line mtight" style="border-bottom-width:0.049em;"></span></span><span style="top:-3.384em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqs" style=""><span class="mord mtight" style="">8</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.344em;"><span></span></span></span></span></span><span class="mclose nulldelimiter sizing reset-size3 size6"></span></span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.82957em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1.0040200000000001em;vertical-align:0em;"></span><span class="mord coloredeq eql" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord coloredeq eqr" style="">2</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.0040200000000001em;"><span style="top:-3.4130000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">−</span><span class="mord mtight" style=""><span class="mopen nulldelimiter sizing reset-size3 size6"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8443142857142858em;"><span style="top:-2.656em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqw" style="">n</span></span></span></span></span><span style="top:-3.2255000000000003em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line mtight" style="border-bottom-width:0.049em"></span></span><span style="top:-3.384em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqs" style="">8</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.344em;"><span></span></span></span></span></span><span class="mclose nulldelimiter sizing reset-size3 size6"></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></p>
<p>残りのヘッドの勾配は幾何学的に連続しており、その比率は上記と同じです。</p>
<p>たとえば、ヘッドの数がの場合、<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord coloredeq eqs" style=""><span class="mord" style="">8</span></span></span></span></span></span>スロープは <span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:2.00744em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord coloredeq eqr" style=""><span class="mord" style="">2</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.740108em;"><span style="top:-2.9890000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord coloredeq eqr" style=""><span class="mord" style="">2</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.740108em;"><span style="top:-2.9890000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqr" style=""><span class="mord mtight" style="">2</span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="minner">…</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord coloredeq eqr" style=""><span class="mord" style="">2</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.740108em;"><span style="top:-2.9890000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight coloredeq eqs" style=""><span class="mord mtight" style="">8</span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></span></p>

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        <div class='code'>
            <div class="highlight"><pre><span class="lineno">43</span><span class="k">def</span> <span class="nf">get_slopes</span><span class="p">(</span><span class="n">n_heads</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span></pre></div>
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            <p>2 <code  class="highlight"><span></span><span class="n">n_heads</span></code>
 の累乗に最も近いものを求めます。が 2 <code  class="highlight"><span></span><span class="n">n_heads</span></code>
 の累乗でない場合は、まず 2 に最も近い (小さな) 累乗までの勾配を計算し、次に残りの勾配を加算します</p>。

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        <div class='code'>
            <div class="highlight"><pre><span class="lineno">62</span>    <span class="n">n</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">**</span> <span class="n">math</span><span class="o">.</span><span class="n">floor</span><span class="p">(</span><span class="n">math</span><span class="o">.</span><span class="n">log2</span><span class="p">(</span><span class="n">n_heads</span><span class="p">))</span></pre></div>
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            <p><span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.9540200000000001em;vertical-align:0em;"></span><span class="mord coloredeq eql" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord coloredeq eqr" style="">2</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9540200000000001em;"><span style="top:-3.363em;margin-right:0.05em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">−</span><span class="mord mtight" style=""><span class="mopen nulldelimiter sizing reset-size3 size6"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8443142857142858em;"><span style="top:-2.656em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqw" style="">n</span></span></span></span></span><span style="top:-3.2255000000000003em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line mtight" style="border-bottom-width:0.049em"></span></span><span style="top:-3.384em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mtight coloredeq eqs" style="">8</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.344em;"><span></span></span></span></span></span><span class="mclose nulldelimiter sizing reset-size3 size6"></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></p>

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        <div class='code'>
            <div class="highlight"><pre><span class="lineno">64</span>    <span class="n">m_0</span> <span class="o">=</span> <span class="mf">2.0</span> <span class="o">**</span> <span class="p">(</span><span class="o">-</span><span class="mf">8.0</span> <span class="o">/</span> <span class="n">n</span><span class="p">)</span></pre></div>
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    <div class='section' id='section-4'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-4'>#</a>
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            <p><span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.14846em;vertical-align:-0.19444em;"></span><span class="mord"><span class="mord coloredeq eqr" style=""><span class="mord" style="">2</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9540200000000001em;"><span style="top:-3.363em;margin-right:0.05em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight">1</span><span class="mord mtight"><span class="mopen nulldelimiter sizing reset-size3 size6"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8443142857142858em;"><span style="top:-2.656em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqw" style=""><span class="mord mathnormal mtight" style="">n</span></span></span></span></span><span style="top:-3.2255000000000003em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line mtight" style="border-bottom-width:0.049em;"></span></span><span style="top:-3.384em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqs" style=""><span class="mord mtight" style="">8</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.344em;"><span></span></span></span></span></span><span class="mclose nulldelimiter sizing reset-size3 size6"></span></span></span></span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord coloredeq eqr" style=""><span class="mord" style="">2</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9540200000000001em;"><span style="top:-3.363em;margin-right:0.05em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight coloredeq eqr" style=""><span class="mord mtight" style="">2</span></span><span class="mord mtight"><span class="mopen nulldelimiter sizing reset-size3 size6"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8443142857142858em;"><span style="top:-2.656em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqw" style=""><span class="mord mathnormal mtight" style="">n</span></span></span></span></span><span style="top:-3.2255000000000003em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line mtight" style="border-bottom-width:0.049em;"></span></span><span style="top:-3.384em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqs" style=""><span class="mord mtight" style="">8</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.344em;"><span></span></span></span></span></span><span class="mclose nulldelimiter sizing reset-size3 size6"></span></span></span></span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord coloredeq eqr" style=""><span class="mord" style="">2</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9540200000000001em;"><span style="top:-3.363em;margin-right:0.05em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight">3</span><span class="mord mtight"><span class="mopen nulldelimiter sizing reset-size3 size6"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8443142857142858em;"><span style="top:-2.656em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqw" style=""><span class="mord mathnormal mtight" style="">n</span></span></span></span></span><span style="top:-3.2255000000000003em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line mtight" style="border-bottom-width:0.049em;"></span></span><span style="top:-3.384em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqs" style=""><span class="mord mtight" style="">8</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.344em;"><span></span></span></span></span></span><span class="mclose nulldelimiter sizing reset-size3 size6"></span></span></span></span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="minner">…</span></span></span></span></span></p>

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        <div class='code'>
            <div class="highlight"><pre><span class="lineno">66</span>    <span class="n">m</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">pow</span><span class="p">(</span><span class="n">m_0</span><span class="p">,</span> <span class="n">torch</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span> <span class="o">+</span> <span class="n">n</span><span class="p">))</span></pre></div>
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                <a href='#section-5'>#</a>
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            <p><code  class="highlight"><span></span><span class="n">n_heads</span></code>
が 2 の累乗でない場合は、残りの勾配を加算します。残りの勾配を計算します <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.46528em;vertical-align:0em;"></span><span class="mord coloredeq eqw" style=""><span class="mord mathnormal" style="">n</span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">∗</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord coloredeq eqr" style=""><span class="mord" style="">2</span></span></span></span></span></span> (以前に追加された勾配は除きます)。そして、<code  class="highlight"><span></span><span class="n">n_heads</span></code>
上の斜面を選んでください</p>.

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        <div class='code'>
            <div class="highlight"><pre><span class="lineno">71</span>    <span class="k">if</span> <span class="n">n</span> <span class="o">&lt;</span> <span class="n">n_heads</span><span class="p">:</span></pre></div>
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    <div class='section' id='section-6'>
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            <div class='section-link'>
                <a href='#section-6'>#</a>
            </div>
            <p><span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.9540200000000001em;vertical-align:0em;"></span><span class="mord"><span class="mord coloredeq eqr" style=""><span class="mord" style="">2</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9540200000000001em;"><span style="top:-3.363em;margin-right:0.05em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight"><span class="mopen nulldelimiter sizing reset-size3 size6"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8443142857142858em;"><span style="top:-2.656em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqr" style=""><span class="mord mtight" style="">2</span></span><span class="mord mtight coloredeq eqw" style=""><span class="mord mathnormal mtight" style="">n</span></span></span></span></span><span style="top:-3.2255000000000003em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line mtight" style="border-bottom-width:0.049em;"></span></span><span style="top:-3.384em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqs" style=""><span class="mord mtight" style="">8</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.344em;"><span></span></span></span></span></span><span class="mclose nulldelimiter sizing reset-size3 size6"></span></span></span></span></span></span></span></span></span></span></span></span></span></span></p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">73</span>        <span class="n">m_hat_0</span> <span class="o">=</span> <span class="mf">2.0</span> <span class="o">**</span> <span class="p">(</span><span class="o">-</span><span class="mf">4.0</span> <span class="o">/</span> <span class="n">n</span><span class="p">)</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-7'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-7'>#</a>
            </div>
            <p><span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.14846em;vertical-align:-0.19444em;"></span><span class="mord"><span class="mord coloredeq eqr" style=""><span class="mord" style="">2</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9540200000000001em;"><span style="top:-3.363em;margin-right:0.05em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight">1</span><span class="mord mtight"><span class="mopen nulldelimiter sizing reset-size3 size6"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8443142857142858em;"><span style="top:-2.656em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqr" style=""><span class="mord mtight" style="">2</span></span><span class="mord mtight coloredeq eqw" style=""><span class="mord mathnormal mtight" style="">n</span></span></span></span></span><span style="top:-3.2255000000000003em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line mtight" style="border-bottom-width:0.049em;"></span></span><span style="top:-3.384em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqs" style=""><span class="mord mtight" style="">8</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.344em;"><span></span></span></span></span></span><span class="mclose nulldelimiter sizing reset-size3 size6"></span></span></span></span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord coloredeq eqr" style=""><span class="mord" style="">2</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9540200000000001em;"><span style="top:-3.363em;margin-right:0.05em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight">3</span><span class="mord mtight"><span class="mopen nulldelimiter sizing reset-size3 size6"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8443142857142858em;"><span style="top:-2.656em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqr" style=""><span class="mord mtight" style="">2</span></span><span class="mord mtight coloredeq eqw" style=""><span class="mord mathnormal mtight" style="">n</span></span></span></span></span><span style="top:-3.2255000000000003em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line mtight" style="border-bottom-width:0.049em;"></span></span><span style="top:-3.384em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqs" style=""><span class="mord mtight" style="">8</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.344em;"><span></span></span></span></span></span><span class="mclose nulldelimiter sizing reset-size3 size6"></span></span></span></span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord coloredeq eqr" style=""><span class="mord" style="">2</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9540200000000001em;"><span style="top:-3.363em;margin-right:0.05em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight">5</span><span class="mord mtight"><span class="mopen nulldelimiter sizing reset-size3 size6"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8443142857142858em;"><span style="top:-2.656em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqr" style=""><span class="mord mtight" style="">2</span></span><span class="mord mtight coloredeq eqw" style=""><span class="mord mathnormal mtight" style="">n</span></span></span></span></span><span style="top:-3.2255000000000003em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line mtight" style="border-bottom-width:0.049em;"></span></span><span style="top:-3.384em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight coloredeq eqs" style=""><span class="mord mtight" style="">8</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.344em;"><span></span></span></span></span></span><span class="mclose nulldelimiter sizing reset-size3 size6"></span></span></span></span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="minner">…</span></span></span></span></span>なお、<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord coloredeq eqr" style=""><span class="mord" style="">2</span></span></span></span></span></span>以前にスロープが追加されないように対策を講じています。</p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">76</span>        <span class="n">m_hat</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">pow</span><span class="p">(</span><span class="n">m_hat_0</span><span class="p">,</span> <span class="n">torch</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span> <span class="o">+</span> <span class="mi">2</span> <span class="o">*</span> <span class="p">(</span><span class="n">n_heads</span> <span class="o">-</span> <span class="n">n</span><span class="p">),</span> <span class="mi">2</span><span class="p">))</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-8'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-8'>#</a>
            </div>
            <p>スロープを残りのスロープと連結します。</p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">78</span>        <span class="n">m</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">cat</span><span class="p">([</span><span class="n">m</span><span class="p">,</span> <span class="n">m_hat</span><span class="p">])</span>
<span class="lineno">79</span>
<span class="lineno">80</span>    <span class="k">return</span> <span class="n">m</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-9'>
        <div class='docs doc-strings'>
            <div class='section-link'>
                <a href='#section-9'>#</a>
            </div>
            <h2>注意バイアスマトリックスの計算</h2>
<ul><li><code  class="highlight"><span></span><span class="n">n_heads</span></code>
アテンションレイヤーのヘッド数です</li>
<li><code  class="highlight"><span></span><span class="n">mask</span></code>
シェイプの注意マスクです <code  class="highlight"><span></span><span class="p">[</span><span class="n">seq_len_q</span><span class="p">,</span> <span class="n">seq_len_k</span><span class="p">]</span></code>
</li></ul>
<p>これにより、AliBi <code  class="highlight"><span></span><span class="p">[</span><span class="n">seq_len_q</span><span class="p">,</span> <span class="n">seq_len_k</span><span class="p">,</span> <span class="n">n_heads</span><span class="p">,</span> <span class="p">]</span></code>
 の注意バイアスが入った形状のマトリックスが返されます。</p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">83</span><span class="nd">@torch</span><span class="o">.</span><span class="n">no_grad</span><span class="p">()</span>
<span class="lineno">84</span><span class="k">def</span> <span class="nf">get_alibi_biases</span><span class="p">(</span><span class="n">n_heads</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">mask</span><span class="p">:</span> <span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span><span class="p">):</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-10'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-10'>#</a>
            </div>
            <p><span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord coloredeq eqv" style=""><span class="mord mathnormal" style="">m</span></span></span></span></span></span>各ヘッドのスロープを取得</p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">95</span>    <span class="n">m</span> <span class="o">=</span> <span class="n">get_slopes</span><span class="p">(</span><span class="n">n_heads</span><span class="p">)</span><span class="o">.</span><span class="n">to</span><span class="p">(</span><span class="n">mask</span><span class="o">.</span><span class="n">device</span><span class="p">)</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-11'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-11'>#</a>
            </div>
            <p><span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord coloredeq eqm" style=""><span class="mopen" style="">[</span><span class="mord" style="">0</span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style="">1</span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="minner" style="">…</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal" style="margin-right:0.10903em">N</span><span class="mclose" style="">]</span></span></span></span></span></span>距離の計算ここではマスクを使って距離を計算します。</p>
<p><span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord coloredeq eqm" style=""><span class="mopen" style="">[</span><span class="mord" style="">0</span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord" style="">1</span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="minner" style="">…</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mpunct" style="">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal" style="margin-right:0.10903em">N</span><span class="mclose" style="">]</span></span></span></span></span></span>カジュアルマスクなのでそのまま使えます。<code  class="highlight"><span></span><span class="n">distance</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">mask</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">dtype</span><span class="o">=</span><span class="n">torch</span><span class="o">.</span><span class="n">long</span><span class="p">,</span> <span class="n">device</span><span class="o">=</span><span class="n">mask</span><span class="o">.</span><span class="n">device</span><span class="p">)[</span><span class="kc">None</span><span class="p">,</span> <span class="p">:]</span></code>
</p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">102</span>    <span class="n">distance</span> <span class="o">=</span> <span class="n">mask</span><span class="o">.</span><span class="n">cumsum</span><span class="p">(</span><span class="n">dim</span><span class="o">=-</span><span class="mi">1</span><span class="p">)</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-12'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-12'>#</a>
            </div>
            <p>それらをペアごとに乗算して、AliBi バイアスマトリックスを求めます。</p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">105</span>    <span class="k">return</span> <span class="n">distance</span><span class="p">[:,</span> <span class="p">:,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">*</span> <span class="n">m</span><span class="p">[</span><span class="kc">None</span><span class="p">,</span> <span class="kc">None</span><span class="p">,</span> <span class="p">:]</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-13'>
        <div class='docs doc-strings'>
            <div class='section-link'>
                <a href='#section-13'>#</a>
            </div>
            <h2>線形バイアスによる注意 (AliBi)</h2>
<p><a href="../mha.html">マルチヘッドアテンションを無効にします</a>。</p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">108</span><span class="k">class</span> <span class="nc">AlibiMultiHeadAttention</span><span class="p">(</span><span class="n">MultiHeadAttention</span><span class="p">):</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-14'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-14'>#</a>
            </div>
            
        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">115</span>    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">heads</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">d_model</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">dropout_prob</span><span class="p">:</span> <span class="nb">float</span> <span class="o">=</span> <span class="mf">0.1</span><span class="p">):</span>
<span class="lineno">116</span>        <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span><span class="n">heads</span><span class="p">,</span> <span class="n">d_model</span><span class="p">,</span> <span class="n">dropout_prob</span><span class="p">)</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-15'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-15'>#</a>
            </div>
            <p>AliBi にバイアスをキャッシュするには</p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">119</span>        <span class="bp">self</span><span class="o">.</span><span class="n">alibi_biases</span> <span class="o">=</span> <span class="kc">None</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-16'>
        <div class='docs doc-strings'>
            <div class='section-link'>
                <a href='#section-16'>#</a>
            </div>
            <p><code  class="highlight"><span></span><span class="n">query</span></code>
、<code  class="highlight"><span></span><span class="n">key</span></code>
<code  class="highlight"><span></span><span class="n">value</span></code>
およびは、<em>クエリ</em>、<em>キー</em>、<em>および値のベクトルのコレクションを格納するテンソルです</em>。形があります<code  class="highlight"><span></span><span class="p">[</span><span class="n">seq_len</span><span class="p">,</span> <span class="n">batch_size</span><span class="p">,</span> <span class="n">d_model</span><span class="p">]</span></code>
。</p>
<p><code  class="highlight"><span></span><span class="n">mask</span></code>
<code  class="highlight"><span></span><span class="p">[</span><span class="n">seq_len</span><span class="p">,</span> <span class="n">seq_len</span><span class="p">,</span> <span class="n">batch_size</span><span class="p">]</span></code>
形状があり、バッチの場合<code  class="highlight"><span></span><span class="n">b</span></code>
、<code  class="highlight"><span></span><span class="n">mask</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">,</span> <span class="n">b</span><span class="p">]</span></code>
<code  class="highlight"><span></span><span class="n">i</span></code>
その位置のクエリがその位置のキー値にアクセスできるかどうかを示します。<code  class="highlight"><span></span><span class="n">j</span></code>
</p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">121</span>    <span class="k">def</span> <span class="nf">forward</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">*</span><span class="p">,</span>
<span class="lineno">122</span>                <span class="n">query</span><span class="p">:</span> <span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span><span class="p">,</span>
<span class="lineno">123</span>                <span class="n">key</span><span class="p">:</span> <span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span><span class="p">,</span>
<span class="lineno">124</span>                <span class="n">value</span><span class="p">:</span> <span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span><span class="p">,</span>
<span class="lineno">125</span>                <span class="n">mask</span><span class="p">:</span> <span class="n">Optional</span><span class="p">[</span><span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">):</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-17'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-17'>#</a>
            </div>
            <p>AliBi は因果マスクでのみ機能します。</p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">137</span>        <span class="k">assert</span> <span class="n">mask</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span>
<span class="lineno">138</span>        <span class="k">assert</span> <span class="n">mask</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">==</span> <span class="n">mask</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="ow">and</span> <span class="n">mask</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">==</span> <span class="mi">1</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-18'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-18'>#</a>
            </div>
            <p><code  class="highlight"><span></span><span class="n">query</span></code>
、<code  class="highlight"><span></span><span class="n">key</span></code>
<code  class="highlight"><span></span><span class="n">value</span></code>
そして形がある <code  class="highlight"><span></span><span class="p">[</span><span class="n">seq_len</span><span class="p">,</span> <span class="n">batch_size</span><span class="p">,</span> <span class="n">d_model</span><span class="p">]</span></code>
</p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">141</span>        <span class="n">seq_len</span><span class="p">,</span> <span class="n">batch_size</span><span class="p">,</span> <span class="n">_</span> <span class="o">=</span> <span class="n">query</span><span class="o">.</span><span class="n">shape</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-19'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-19'>#</a>
            </div>
            <p>マスクに頭部の寸法を追加し、形状を確認します。</p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">144</span>        <span class="n">mask</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">prepare_mask</span><span class="p">(</span><span class="n">mask</span><span class="p">,</span> <span class="n">query</span><span class="o">.</span><span class="n">shape</span><span class="p">,</span> <span class="n">key</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-20'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-20'>#</a>
            </div>
            <p><code  class="highlight"><span></span><span class="n">query</span></code>
<code  class="highlight"><span></span><span class="n">key</span></code>
<code  class="highlight"><span></span><span class="n">value</span></code>
注意力計算の準備をして<code  class="highlight"><span></span><span class="p">[</span><span class="n">seq_len</span><span class="p">,</span> <span class="n">batch_size</span><span class="p">,</span> <span class="n">heads</span><span class="p">,</span> <span class="n">d_k</span><span class="p">]</span></code>
これで形ができあがります。</p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">148</span>        <span class="n">query</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">query</span><span class="p">(</span><span class="n">query</span><span class="p">)</span>
<span class="lineno">149</span>        <span class="n">key</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">key</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
<span class="lineno">150</span>        <span class="n">value</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">value</span><span class="p">(</span><span class="n">value</span><span class="p">)</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-21'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-21'>#</a>
            </div>
            <p><span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.043548em;vertical-align:-0.19444em;"></span><span class="mord coloredeq eqo" style=""><span class="mord mathnormal" style="">Q</span><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.849108em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style="">⊤</span></span></span></span></span></span></span></span></span></span></span></span></span>アテンションスコアを計算します。<code  class="highlight"><span></span><span class="p">[</span><span class="n">seq_len</span><span class="p">,</span> <span class="n">seq_len</span><span class="p">,</span> <span class="n">batch_size</span><span class="p">,</span> <span class="n">heads</span><span class="p">]</span></code>
これにより形状のテンソルが得られます</p>。

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">154</span>        <span class="n">scores</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">get_scores</span><span class="p">(</span><span class="n">query</span><span class="p">,</span> <span class="n">key</span><span class="p">)</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-22'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-22'>#</a>
            </div>
            <p>スケールスコア <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.633028em;vertical-align:-0.538em;"></span><span class="mord coloredeq eqj" style=""><span class="mord" style=""><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.095028em;"><span style="top:-2.5864385em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord sqrt mtight" style=""><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8622307142857143em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mtight" style="padding-left:0.833em"><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqt" style="">d</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em;"><span style="top:-2.3487714285714287em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mathnormal mtight" style="margin-right:0.03148em">k</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15122857142857138em;"><span></span></span></span></span></span></span></span></span><span style="top:-2.8222307142857144em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail mtight" style="min-width:0.853em;height:1.08em"><svg height="1.08em" preserveaspectratio="xMinYMin slice" viewbox="0 0 400000 1080" width="400em" xmlns="http://www.w3.org/2000/svg"><path d="M95,702
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c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
c69,-144,104.5,-217.7,106.5,-221
l0 -0
c5.3,-9.3,12,-14,20,-14
H400000v40H845.2724
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z"></path></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.17776928571428574em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.446108em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqo" style="">Q</span><span class="mord mtight coloredeq eqo" style=""><span class="mord mathnormal mtight" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9270285714285713em;"><span style="top:-2.931em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style="">⊤</span></span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.538em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></span></p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">157</span>        <span class="n">scores</span> <span class="o">*=</span> <span class="bp">self</span><span class="o">.</span><span class="n">scale</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-23'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-23'>#</a>
            </div>
            <p>キャッシュされていない場合はAliBiバイアスを作成する</p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">160</span>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">alibi_biases</span> <span class="ow">is</span> <span class="kc">None</span> <span class="ow">or</span> <span class="bp">self</span><span class="o">.</span><span class="n">alibi_biases</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">&lt;</span> <span class="n">seq_len</span><span class="p">:</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-24'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-24'>#</a>
            </div>
            <p><code  class="highlight"><span></span><span class="n">mask</span></code>
<a href="seq_len, seq_len, 1, 1">図形は連番、連番、1、</a> 1です</p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">162</span>            <span class="bp">self</span><span class="o">.</span><span class="n">alibi_biases</span> <span class="o">=</span> <span class="n">get_alibi_biases</span><span class="p">(</span><span class="n">scores</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="n">mask</span><span class="p">[:,</span> <span class="p">:,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">])</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-25'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-25'>#</a>
            </div>
            <p>AliBi バイアスをアテンションスコアに追加します。AliBi <code  class="highlight"><span></span><span class="p">[</span><span class="n">seq_len</span><span class="p">,</span> <span class="n">seq_len</span><span class="p">,</span> <span class="n">n_heads</span><span class="p">]</span></code>
 <code  class="highlight"><span></span><span class="n">scores</span></code>
 バイアスには形と形がある <code  class="highlight"><span></span><span class="p">[</span><span class="n">seq_len</span><span class="p">,</span> <span class="n">seq_len</span><span class="p">,</span> <span class="n">batch_size</span><span class="p">,</span> <span class="n">n_heads</span><span class="p">]</span></code>
</p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">167</span>        <span class="n">scores</span> <span class="o">+=</span> <span class="bp">self</span><span class="o">.</span><span class="n">alibi_biases</span><span class="p">[:</span><span class="n">seq_len</span><span class="p">,</span> <span class="p">:</span><span class="n">seq_len</span><span class="p">,</span> <span class="kc">None</span><span class="p">,</span> <span class="p">:]</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-26'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-26'>#</a>
            </div>
            <p>マスクを適用</p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">170</span>        <span class="n">scores</span> <span class="o">=</span> <span class="n">scores</span><span class="o">.</span><span class="n">masked_fill</span><span class="p">(</span><span class="n">mask</span> <span class="o">==</span> <span class="mi">0</span><span class="p">,</span> <span class="nb">float</span><span class="p">(</span><span class="s1">&#39;-inf&#39;</span><span class="p">))</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-27'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-27'>#</a>
            </div>
            <p><span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord coloredeq eqp" style=""><span class="mord mathnormal" style="">so</span><span class="mord mathnormal" style="margin-right:0.10764em">f</span><span class="mord mathnormal" style="">t</span><span class="mord" style=""><span class="mord mathnormal coloredeq eqv" style="">m</span></span><span class="mord mathnormal" style="">a</span><span class="mord mathnormal" style="">x</span></span></span></span></span></span>キーシーケンス次元に沿って注目 <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:3.0000299999999998em;vertical-align:-1.25003em;"></span><span class="mord coloredeq eqe" style=""><span class="mord" style=""><span class="mop op-limits" style=""><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.6944399999999998em;"><span style="top:-2.20556em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight" style="">se</span><span class="mord mathnormal mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span><span class="mop" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqp" style="">so</span><span class="mord mathnormal coloredeq eqp" style="margin-right:0.10764em">f</span><span class="mord mathnormal coloredeq eqp" style="">t</span><span class="mord coloredeq eqp" style=""><span class="mord mathnormal coloredeq eqv" style="">m</span></span><span class="mord mathnormal coloredeq eqp" style="">a</span><span class="mord mathnormal coloredeq eqp" style="">x</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.030548em;"><span></span></span></span></span></span></span><span class="mord" style=""><span class="delimsizing size4" style=""><span style="">(</span></span></span><span class="mord" style=""><span class="mord coloredeq eqj" style=""><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.095028em;"><span style="top:-2.5864385em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord sqrt mtight" style=""><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8622307142857143em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mtight" style="padding-left:0.833em"><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqt" style="">d</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em;"><span style="top:-2.3487714285714287em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mathnormal mtight" style="margin-right:0.03148em">k</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15122857142857138em;"><span></span></span></span></span></span></span></span></span><span style="top:-2.8222307142857144em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail mtight" style="min-width:0.853em;height:1.08em"><svg height="1.08em" preserveaspectratio="xMinYMin slice" viewbox="0 0 400000 1080" width="400em" xmlns="http://www.w3.org/2000/svg"><path d="M95,702
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c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
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M834 80h400000v40h-400000z"></path></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.17776928571428574em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.446108em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqo" style="">Q</span><span class="mord mtight coloredeq eqo" style=""><span class="mord mathnormal mtight" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9270285714285713em;"><span style="top:-2.931em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style="">⊤</span></span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.538em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="mord" style=""><span class="delimsizing size4" style=""><span style="">)</span></span></span></span></span></span></span></span></p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">174</span>        <span class="n">attn</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">softmax</span><span class="p">(</span><span class="n">scores</span><span class="p">)</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-28'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-28'>#</a>
            </div>
            <p>ドロップアウトを適用</p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">177</span>        <span class="n">attn</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">dropout</span><span class="p">(</span><span class="n">attn</span><span class="p">)</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-29'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-29'>#</a>
            </div>
            <p>値による乗算 <span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:3.0000299999999998em;vertical-align:-1.25003em;"></span><span class="mord coloredeq eqe" style=""><span class="mord" style=""><span class="mop op-limits" style=""><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.6944399999999998em;"><span style="top:-2.20556em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight" style="">se</span><span class="mord mathnormal mtight" style="margin-right:0.03588em">q</span></span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span><span class="mop" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqp" style="">so</span><span class="mord mathnormal coloredeq eqp" style="margin-right:0.10764em">f</span><span class="mord mathnormal coloredeq eqp" style="">t</span><span class="mord coloredeq eqp" style=""><span class="mord mathnormal coloredeq eqv" style="">m</span></span><span class="mord mathnormal coloredeq eqp" style="">a</span><span class="mord mathnormal coloredeq eqp" style="">x</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.030548em;"><span></span></span></span></span></span></span><span class="mord" style=""><span class="delimsizing size4" style=""><span style="">(</span></span></span><span class="mord" style=""><span class="mord coloredeq eqj" style=""><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.5261079999999998em;"><span style="top:-2.25278em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style=""><span class="mord sqrt" style=""><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.85722em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="padding-left:0.833em"><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqt" style="">d</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mathnormal mtight" style="margin-right:0.03148em">k</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-2.81722em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail" style="min-width:0.853em;height:1.08em"><svg height="1.08em" preserveaspectratio="xMinYMin slice" viewbox="0 0 400000 1080" width="400em" xmlns="http://www.w3.org/2000/svg"><path d="M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
c69,-144,104.5,-217.7,106.5,-221
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H400000v40H845.2724
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z"></path></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.18278000000000005em;"><span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style=""><span class="mord" style=""><span class="mord mathnormal coloredeq eqo" style="">Q</span><span class="mord coloredeq eqo" style=""><span class="mord mathnormal" style="margin-right:0.07153em">K</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.849108em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style="">⊤</span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.93em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span><span class="mord" style=""><span class="delimsizing size4" style=""><span style="">)</span></span></span></span><span class="mord mathnormal" style="margin-right:0.22222em;">V</span></span></span></span></span></span></p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">181</span>        <span class="n">x</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">einsum</span><span class="p">(</span><span class="s2">&quot;ijbh,jbhd-&gt;ibhd&quot;</span><span class="p">,</span> <span class="n">attn</span><span class="p">,</span> <span class="n">value</span><span class="p">)</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-30'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-30'>#</a>
            </div>
            <p>複数のヘッドを連結</p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">184</span>        <span class="n">x</span> <span class="o">=</span> <span class="n">x</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">seq_len</span><span class="p">,</span> <span class="n">batch_size</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">)</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-31'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-31'>#</a>
            </div>
            <p>出力レイヤー</p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">187</span>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">output</span><span class="p">(</span><span class="n">x</span><span class="p">)</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-32'>
        <div class='docs doc-strings'>
            <div class='section-link'>
                <a href='#section-32'>#</a>
            </div>
            <p>スロープを確認できる簡単なテスト機能。</p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">190</span><span class="k">def</span> <span class="nf">_test_alibi</span><span class="p">():</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-33'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-33'>#</a>
            </div>
            
        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">194</span>    <span class="n">inspect</span><span class="p">(</span><span class="n">get_slopes</span><span class="p">(</span><span class="mi">12</span><span class="p">)</span><span class="o">.</span><span class="n">tolist</span><span class="p">(),</span> <span class="n">_n</span><span class="o">=-</span><span class="mi">1</span><span class="p">)</span>
<span class="lineno">195</span>    <span class="kn">from</span> <span class="nn">labml_nn.transformers.utils</span> <span class="kn">import</span> <span class="n">subsequent_mask</span>
<span class="lineno">196</span>
<span class="lineno">197</span>    <span class="n">mask</span> <span class="o">=</span> <span class="n">subsequent_mask</span><span class="p">(</span><span class="mi">8</span><span class="p">)[:,</span> <span class="p">:,</span> <span class="mi">0</span><span class="p">]</span>
<span class="lineno">198</span>    <span class="n">inspect</span><span class="p">(</span><span class="n">mask</span><span class="p">)</span>
<span class="lineno">199</span>
<span class="lineno">200</span>    <span class="n">inspect</span><span class="p">(</span><span class="n">get_alibi_biases</span><span class="p">(</span><span class="mi">12</span><span class="p">,</span> <span class="n">mask</span><span class="p">)[:,</span> <span class="p">:,</span> <span class="mi">3</span><span class="p">],</span> <span class="n">_n</span><span class="o">=-</span><span class="mi">1</span><span class="p">)</span></pre></div>
        </div>
    </div>
    <div class='section' id='section-34'>
        <div class='docs'>
            <div class='section-link'>
                <a href='#section-34'>#</a>
            </div>
            <p></p>

        </div>
        <div class='code'>
            <div class="highlight"><pre><span class="lineno">204</span><span class="k">if</span> <span class="vm">__name__</span> <span class="o">==</span> <span class="s1">&#39;__main__&#39;</span><span class="p">:</span>
<span class="lineno">205</span>    <span class="n">_test_alibi</span><span class="p">()</span></pre></div>
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